In some embodiments, a body cavity shape of a subject is reconstructed based on intrabody measurements of at least one property of an electromagnetic field by an intrabody probe (for example, a catheter probe) moving within a plurality of electrical fields intersecting the body cavity. In some embodiments, the electrical fields are generated at least in part from electrodes positioned in close proximity, for example, within 1 cm, of the body cavity. In some embodiments, the body cavity is a chamber of a heart (for example, a left atrium or left ventricle), and the electrodes used to generate the electrical field are positioned in the coronary sinus, a large vein occupying the groove between the left atrium and left ventricle. In some embodiments, known distances between measuring electrodes are used in guiding reconstruction, potentially overcoming difficulties of reconstruction from measurements of non-linear electrical fields.